Thanks -
It appears my source might have been incomplete. Checking back, they seem to have considered 'Withdrawn' as not meeting the criteria of 'entered a Formula One Championship race'.
Depending on interpretation, some sources for the 1962 US GP report that 'Scuderia Ferrari were entered for the race as #1, 2 and 3, but nominated neither cars nor drivers.' which I think is why Mairesse is also not on their list.
But - with all that, there is still one more driver that entered a championship race with number one on their car, that has not been mentioned yet.
To summarise where we are:
Which Formula One Champions never raced with a number one on their car?
Mike Hawthorn,
Jochen Rindt,
Nigel Mansell,
Nico Rosberg.
And which drivers entered a Formula One Championship race with number one on their car, despite never being a champion?
Graham Whitehead – 1952 British Grand Prix
Lance Macklin ran - 1953 British Grand Prix
José Froilán González - 1954 German Grand Prix
Stirling Moss - 1958 Dutch Grand Prix
Peter Collins – 1958 British Grand Prix
Jean Behra - 1959 Dutch Grand Prix
Willy Mairesse - 1962 US Grand Prix (did not attend)
Andre Pilette - 1964 Monaco Grand Prix (withdrawn)
Chris Amon - 1967 Belgian Grand Prix
Jean-Pierre Beltoise - 1967 Monaco Grand Prix (DNQ) and 1968 Monaco Grand Prix
Ludovico Scarfiotti - 1967 French Grand Prix (withdrawn)
Pedro Rodr?*guez - 1970 Belgian Grand Prix and 1970 Dutch Grand Pri
Ronnie Peterson - 1974 Season Long
John Watson – 1985 European Grand Prix
Plus - one more driver who has not been mentioned......